No you will need to integrate cos²θ with respect to θ of course. You are integrating over a volume, in Cartesian coordinates the volume element would be dxdydz. However we're not using Cartesian coordinates, but spherical coordinates. Therefore you need to integrate over the volume element in spherical coordinates.

Staff: Mentor

To put what Cyosis said (in post #2) in other words, the normalization integral is a volume integral:

[tex]\int {\int {\int {|\psi_{210}|^2 dV}}} = 1[/tex]

where dV is a volume element. If you were doing the integral in rectangular coordinates, dV would be dx dy dz. But you're actually using spherical polar coordinates. What's dV in spherical polar coordinates?

Is it bothering you because what you tried gave you 0 as the answer? If so, you integrated correctly. That factor shouldn't be there.

Of course I forgot about the complex conjugate when normalising the wavefunctions, so essentially this will get rid of the exponential of the wavefunction im taking the complex conjugate of, but there will still be an exponential term in the integral. Im not sure where this is going..

U_210 had an exponential in the integral as well. What's the problem? The complex exponential disappears, but the real exponential, just as for u210, stays.

What I'm trying to do is integrate the following:

∫exp(φ).exp(iφ) dφ

Before, I could easily integrate the exponential because I had the identity, but when I try integrating this I get a factor of 'i'. My maths is terrible, this is partly the reason why I cant see the problem very well.

As Vela said that term shouldn't be there. Remember [itex]|\psi|^2=\psi^* \psi[/itex].

That said I find it a little odd that you aren't able to compute a simple exponential function and I suggest you brush up your calculus immediately or you will run into a lot of difficulties during your QM course.

Before, I could easily integrate the exponential because I had the identity, but when I try integrating this I get a factor of 'i'. My maths is terrible, this is partly the reason why I cant see the problem very well.

If you integrate that expression you will indeed get a factor 'i'. However to not confuse you I will say it again, those exponentials shouldn't be there in the first place!

As Vela said that term shouldn't be there. Remember [itex]|\psi|^2=\psi^* \psi[/itex].

That said I find it a little odd that you aren't able to compute a simple exponential function and I suggest you brush up your calculus immediately or you will run into a lot of difficulties during your QM course.

If you integrate that expression you will indeed get a factor 'i'. However to not confuse you I will say it again, those exponentials shouldn't be there in the first place!

Wow! that was very stupid of me! The mix up was with the complex conjugate, very often examples in QM from my course that involve normalisation of a wavefunction dont have complex numbers. After fixing that I got a factor of Pi, hence normalising the wavefunction. I assume the limits are from 0 to Pi